Permutations with Repeats 2.4

Up to now each element has been unique.
For example there are 6! different arrangements of the word PENCIL because each letter is different.
We found there were only 12 different arrangements of the word TOOL because the O is repeated.
It cannot be 4! to give us 24 different arrangements but we can divide 24/2 because of the 2 O's

To find the number of arrangements with repeats is n!/(a!b!) where a and b are the number of elements that are repeated.

How many different arrangements are there of the city TORONTO?
7!/(3!2!) = 420

We can use this principal for finding the number of ways to follow a pathway.

HW: 

• P 105 # 1,2,5,6,7,9, 12, 15, 16
• Name arrangements (see below)
• Quiz NR3 & MC 6,7,8

Name Arrangements Assignment

How many different ways can you arrange the letters in your name using...

• only your first name?
• only your last name?
• both your first and last name as one "all-together" name?
• both your first and last name as separate names?